Britton Flashcards
What is the scale on the NMR spectra?
Chemical shift - parts per million
What frequency does NMR occur at?
Radiofrequency
What are the selection rules for NMR?
Must possess nuclear spin (only visible for unpaired nucleons meaning I cannot equal zero)
ΔM = +/- 1
What are two examples of Nucleides that do not show an NMR spectra?
12C and 16O
What is a nucleon?
Nucleons have shells of either two protons or two neutrons and must have unpaired nucleons
What equation is used to calculate the magnetic moment of a nucleon?
μ = γ * P
Where:
μ = magnetic moment
γ = Magnetogyric ratio
P = Angular momentum
What happens to the spin states when there’s no external magnetic field?
All states have the same energy - degenerate
When I is greater than 1, what is the magnetic moment known as?
Quadrupolar
How do you calculate the energy change between spin states?
ΔE = hν = hxBo / 2π
What will happen when applying a magnetic field to nucleus?
It will begin to spin AKA Precess
What is the frequency of nuclear precession dependant on?
the strength of the magnetic field and the magnetogyric ratio:
ω = - γBo (rad s-1) where ω = Lamar frequency
where Bo = strength of magnetic field
ν = γBo/2π (Hz)
What are the two spectrometer types and what are their two frequencies?
500Hz = Small molecules 900Hz = Larger molecules such as proteins
what distribution must you consider when determining the average spin of all the nuclei?
Boltzmann distribution
Which equation links the number of up spin and down spin molecules with the Boltzmann distribution?
(N1/2)/(N-1/2) = exp (ΔE/KT)
What is the equation demonstrating the eigenvalue?
Ωψ = ωψ
Where Ω and ω = the operator
ψ = the eigenfunction
What does the Hamiltonian operator demonstrate and which equation links it to the strength of the magnetic field?
Hone spin = - γBoIz
where H has a hat and I has a hat
The Hamiltonian operator demonstrates the energy of the system determining the energy of interaction between the spin and Bo.
What is the eigenvalue for a one-spin hamiltonian?
When I = 1/2
ψ1/2 (m=+1/2) and ψ-1/2 (m=-1/2) so:
Îzψm = mħψm
What is the effect of radiofrequency radiation?
Macroscopic magnetisation (Mo) can be manipulated using rf electromagnetic radiation at the Larmor frequency.
What is the resonance condition?
Radiofrequency has to match Larmor frequency which must also match ΔE between the Alpha and beta levels
What happens after a 90 degree pulse?
equal numbers of alpha and beta state spins - the Mo vector is pointing at the x direction
What happens after a 180 degree pulse?
Inversion of the spin populations, theres more spin down than spin up where the Mo points along the -z axis
What are the two factors used to determine the angles of the RF pulses?
1) Duration of pulse (tp)
2) Power of pulse (B1)
Where duration of pulse is the most common
What equation is used to calculate the angle of the pulse
σ = (360γ/2π) * B1 * tp
How is the vector described?
Mo - macroscopic magnetisation vector
When will an NMR signal be produced?
When the macroscopic magnetisation vector is in the transverse plane
How is an NMR signal produced?
When the macroscopic magnetisation vector is in the transverse plan, faradaic induction is present. All of the nuclei and the Mo will be spinning at the Lamar frequency. As the Mo rotates, a current is induced in a receiver coil - producing an NMR signal. A Fourier transferred into a recognisable signal
At thermal equilibrium, which direction will the macroscopic magnetisation vector (Mo) point in?
the Z direction
Explain free induction decay
The oscillating Mo vector will induce a weak oscillating voltage in the rf coil. This oscillation is known as free induction decay
What is the intensity of the NMR signal linked to?
The amount of the magnetisation vector that Is along the transverse plane. As time increases, the system will relax back to thermal equilibrium and therefore signal intensity will increase.
What four factors affect the appearance of an NMR spectra?
1) Chemical Shift: multiple peaks
2) Spin-Spin coupling: multiplets of peaks
3) Relaxation: peak width and intensity
4) axial and equatorial protons
What factors affect chemical shift?
Not all nuclei will precess in the same frequency
Not all nuclei experience the same magnetic field
Nuclei near electronegative species experience stronger magnetic field than electron donation species
What is the offset frequency?
The macroscopic magnetisation vector is created, each spin within this vector will have it’s own specific resonance, ν. The offset frequency is the difference between this spin resonance and the transmitter frequency.
Ω=ν-νo (Hz)
How is the spin resonance frequency and transmitter frequency related to the chemical shift?
δ = 10^6 (ν-νo)/νo in ppm
What are the two relaxation mechanisms?
T1 and T2
Explain T1 relaxation
When the sample has a magnetic field applied, the alpha and beta states are no longer degenerate. As time goes by, the system reorganises back to it’s initial, non-excited state. This takes a while but is dependant on spin-lattice relaxation time - allowing spins to flip energy until the Boltzmann distribution is met.
What is the origin of spin-lattice relaxation?
- each nucleus has nuclear spin which possesses a magnetic dopole
- nuclear spin depends on magnetic interactions between nuclear magnetic dipole
- Nuclear spins interact with each other through space via dipole coupling which is dependent on the separation (r) and angle (θ)
- Dependant on the rotating correlating time (Tc) because of fluctuating local fields
What is Tc with respect to rotational motion of liquids?
rotational correlation of time - related to time taken for a molecule to completely change orientation - change orientation by 1 rad.
What factors does Tc depend on?
Size of molecule and viscosity of solvent
What is the main function of Tc?
To compare molecules directly
How close do nuclei have to be in order to experience the NOE effect?
3-5 angstrongs
What is the result of a peak that is adjacent and presents with the NOE effect?
1) Increase intensity
2) Decrease intensity
3) Inversion of intensity
Explain W2 relaxation
- When the system has had it’s s states saturated, the system will want to return to thermal equilibrium.
- W2 removes the βIβS states by moving to αIαS states. - - This increases the population difference of the two I states.
- This has a NET increase on the I spin resonance intensity therefore leading to a positive NOE
Explain W0 relaxation
- When the system has had it’s s states saturated, the system will want to return to thermal equilibrium.
- transfer of spin βα to a αβ
- this decreases the population difference across the 2 I transitions
- Decreased NET intensity of the I spin resonance intensity
What is another name for T2 relaxation?
Spin-Spin relaxation
What does T2 relaxation cause?
Decreased lifetime of spin-states and line broadening
What is T2 relaxation caused by?
- Differences produced by inter/intra molecular interactions
- Interactions with Bo
If the T2 is fast, the line is…
Broad
If the T2 is slow, the line is…
thin
What does the line width ΔV depend on?
Magnetic field differences
What does the line width ΔV, arise from?
Imperfections in the state magnetic field (Bo)
Local magnetic fields arise from intra and intermolecular interactions
How long are radiofrequency pulses ordinarily?
5-50μs
What is the difference between the frequency of a TMS signal and an NMR signal?
TMS - 300,000,000 Hz =300 MHz
NMR - 300,002,000 Hz
